Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4645455 | Applied Numerical Mathematics | 2012 | 15 Pages |
Abstract
Two domain decomposition methods for computing eigenvalues and eigenfunctions of the Laplace operator on a bounded domain are presented. The methods are formulated in terms of the Dirichlet-to-Neumann (DtN) and Neumann-to-Dirichlet (NtD) surface integral operators. They are adapted from the DtN and NtD methods for bound states of the Schrödinger equation in R3. A variational principle that enables the usage of the operators is constructed. The variational principle allows the use of discontinuous (in values or derivatives) trial functions. A numerical example presenting the usefulness of the DtN and NtD methods is given.
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